x > 1 のとき
( 1 + 4 x ^ 2 + x ^ 4 ) log x + ( 3 / 2 ) ( 1 - x ^ 4 ) > 0


0 ≦ x [ k ] ≦ π / 2
Σ [ k = 1 , n ] cos x [ k ] = 1
のとき
Σ [ k = 1 , n ] sin x [ k ] ≧ √ ( n - 1 )